Reformulation of the plane wave method to model photonic crystals

doi:10.1364/OE.11.002905

Optics Express

Editor: Michael Duncan
Vol. 11, Iss. 22 — Nov. 3, 2003
pp: 2905–2910

Reformulation of the plane wave method to model photonic crystals

Rossella Zoli, Marco Gnan, Davide Castaldini, Gaetano Bellanca, and Paolo Bassi »View Author Affiliations

Optics Express, Vol. 11, Issue 22, pp. 2905-2910 (2003)
http://dx.doi.org/10.1364/OE.11.002905

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Abstract
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References (13)
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Abstract

A new formulation of the plane-wave method to study the characteristics (dispersion curves and field patterns) of photonic crystal structures is proposed. The expression of the dielectric constant is written using the superposition of two regular lattices, the former for the perfect structure and the latter for the defects. This turns out to be simpler to implement than the classical one, based on the supercell concept. Results on mode coupling effects in two-dimensional photonic crystal waveguides are studied and successfully compared with those provided by a Finite Difference Time Domain method. In particular the approach is shown able to determine the existence of “mini-stop bands” and the field patterns of the various interfering modes.

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(230.7380) Optical devices : Waveguides, channeled

ToC Category:
Research Papers

History
Original Manuscript: September 15, 2003
Revised Manuscript: October 24, 2003
Published: November 3, 2003

Citation
Rossella Zoli, Marco Gnan, Davide Castaldini, Gaetano Bellanca, and Paolo Bassi, "Reformulation of the plane wave method to model photonic crystals," Opt. Express 11, 2905-2910 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-22-2905

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References

K. Sakoda, Optical properties of Photonic Crystals, Springer (2001).
S. G. Johnson, J. D. Joannopoulos, Photonic crystals The Road from Theory to Practice, Kluwer Academic Publishers, (2001).
H. Benisty, �??Modal analysis of optical guides with two-dimensional photonic band gap boundaries,�?? J. Appl. Phys. 79, 7483-7492 (1996). [CrossRef]
P. R. Villeneuve, S. Fan, J. D. Joannopoulos, �??Microcavity in photonic crystals: Mode symmetry, tenability and coupling efficiency,�?? Phy. Rev. B 54, 7837-7842 (1996). [CrossRef]
S. Guo, S. Albin, �??A simple plane wave implementation method for photonic crystal calculations,�?? Opt. Express 11, 167 (2003). [CrossRef] [PubMed]
A.Taflove, Computational electrodynamics �?? The Finite Difference Time-Domain Method, (Artech House, Norwood, MA, 1995).
F. Fogli, J. Pagazaurtundua Alberte, G. Bellanca, P. Bassi, �??Analysis of Finite 2-D Photonic Bandgap Lightwave Devices using the FD-TD Method,�?? Proc. of IEEE-WFOPC 2000, Pavia, June 8-9, 236-241 (2000).
M. Kafesaki, M. Agio, C. M. Soukoulis, �??Waveguides in finite-height two-dimensional photonic crystals,�?? J. Opt. Soc. Am. B 19, 2232 (2002). [CrossRef]
M. Agio, C. M. Soukoulis, �??Ministop bands in single defect photonic crystal waveguides,�?? Phys. Rev. E 64, 055603 (2001). [CrossRef]
S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F . Krauss, R. Houdrè, �??Coupled-mode theory and propagation losses in photonic crystal waveguides,�?? Opt. Express 11, 1490-1496 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490.</a> [CrossRef] [PubMed]
S. Olivier, M. Rattier, H. Benisty, C. Weisbuch, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Osterle, R. Houdrè, �??Mini-stopbands of one-dimensional system: The channel waveguide in a two-dimensional photonic crystal,�?? Phys. Rev. B. 63, 11311 (2001). [CrossRef]
C. J. M. Smith, R. M. De La Rue, M. Rattier ,S. Olivier, H. Benisty, C. Weisbuch, T. F . Krauss, R. Houdrè, U. Osterle �??Coupled guide and cavity in a two-dimensional photonic crystal,�?? Appl. Phys. Lett. 78, 1487-1489 (2001). [CrossRef]
M. Qiu, K. Azizi, A. Karlsson, M. Swillo, B. Jaskorzynska, �??Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,�?? Phy. Rev. B 64, 155113 (2001). [CrossRef]

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[1] K. Sakoda, Optical properties of Photonic Crystals, Springer (2001).

[2] S. G. Johnson, J. D. Joannopoulos, Photonic crystals The Road from Theory to Practice, Kluwer Academic Publishers, (2001).

[3] H. Benisty, �??Modal analysis of optical guides with two-dimensional photonic band gap boundaries,�?? J. Appl. Phys. 79, 7483-7492 (1996). [CrossRef]

[4] P. R. Villeneuve, S. Fan, J. D. Joannopoulos, �??Microcavity in photonic crystals: Mode symmetry, tenability and coupling efficiency,�?? Phy. Rev. B 54, 7837-7842 (1996). [CrossRef]

[5] S. Guo, S. Albin, �??A simple plane wave implementation method for photonic crystal calculations,�?? Opt. Express 11, 167 (2003). [CrossRef] [PubMed]

[6] A.Taflove, Computational electrodynamics �?? The Finite Difference Time-Domain Method, (Artech House, Norwood, MA, 1995).

[7] F. Fogli, J. Pagazaurtundua Alberte, G. Bellanca, P. Bassi, �??Analysis of Finite 2-D Photonic Bandgap Lightwave Devices using the FD-TD Method,�?? Proc. of IEEE-WFOPC 2000, Pavia, June 8-9, 236-241 (2000).

[8] M. Kafesaki, M. Agio, C. M. Soukoulis, �??Waveguides in finite-height two-dimensional photonic crystals,�?? J. Opt. Soc. Am. B 19, 2232 (2002). [CrossRef]

[9] M. Agio, C. M. Soukoulis, �??Ministop bands in single defect photonic crystal waveguides,�?? Phys. Rev. E 64, 055603 (2001). [CrossRef]

[10] S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F . Krauss, R. Houdrè, �??Coupled-mode theory and propagation losses in photonic crystal waveguides,�?? Opt. Express 11, 1490-1496 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490.</a> [CrossRef] [PubMed]

[11] S. Olivier, M. Rattier, H. Benisty, C. Weisbuch, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Osterle, R. Houdrè, �??Mini-stopbands of one-dimensional system: The channel waveguide in a two-dimensional photonic crystal,�?? Phys. Rev. B. 63, 11311 (2001). [CrossRef]

[12] C. J. M. Smith, R. M. De La Rue, M. Rattier ,S. Olivier, H. Benisty, C. Weisbuch, T. F . Krauss, R. Houdrè, U. Osterle �??Coupled guide and cavity in a two-dimensional photonic crystal,�?? Appl. Phys. Lett. 78, 1487-1489 (2001). [CrossRef]

[13] M. Qiu, K. Azizi, A. Karlsson, M. Swillo, B. Jaskorzynska, �??Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,�?? Phy. Rev. B 64, 155113 (2001). [CrossRef]

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Reformulation of the plane wave method to model photonic crystals